Abelian tropical covers

Yoav Len*, Martin Ulirsch, Dmitry Zakharov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

Let 𝔄 be a finite abelian group. In this article, we classify harmonic 𝔄-covers of a tropical curve Γ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on Γ. We give a realizability criterion for harmonic 𝔄-covers by patching local monodromy data in an extended homology group on Γ. As an explicit example, we work out the case 𝔄=ℤ/pℤ and explain how realizability for such covers is related to the nowhere-zero flow problem from graph theory.
Original languageEnglish
Number of pages22
JournalMathematical Proceedings of the Cambridge Philosophical Society
VolumeFirstView
Early online date10 Oct 2023
DOIs
Publication statusE-pub ahead of print - 10 Oct 2023

Keywords

  • Coverings
  • Fundamental group

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